Proportional Aggregation of Preferences for Sequential Decision Making

TL;DR

This paper introduces proportional aggregation rules for fair sequential decision making based on voter preferences, ensuring fair representation across rounds, and demonstrates their effectiveness through empirical experiments on synthetic and real-world data.

Contribution

It proposes new axioms for proportional representation in sequential decisions and evaluates three voting rules that satisfy these axioms, including online and offline methods.

Findings

Sequential Phragmén makes decisions online effectively.

The rules achieve fairer utility distribution across demographics.

Empirical results show improved fairness in decision outcomes.

Abstract

We study the problem of fair sequential decision making given voter preferences. In each round, a decision rule must choose a decision from a set of alternatives where each voter reports which of these alternatives they approve. Instead of going with the most popular choice in each round, we aim for proportional representation across rounds, using axioms inspired by the multi-winner voting literature. The axioms require that every group of $\alpha\%$ of the voters that agrees in every round (i.e., approves a common alternative), must approve at least $\alpha\%$ of the decisions. A stronger version of the axioms requires that every group of $\alpha\%$ of the voters that agrees in a $\beta$ fraction of rounds must approve $\beta\cdot\alpha\%$ of the decisions. We show that three attractive voting rules satisfy axioms of this style. One of them (Sequential Phragm\'en) makes its decisions online, and the other two satisfy strengthened versions of the axioms but make decisions semi-online (Method of Equal Shares) or fully offline (Proportional Approval Voting). We present empirical results for these rules based on synthetic data and U.S. political elections. We also run experiments using the moral machine dataset about ethical dilemmas: We train preference models on user responses from different countries and let the models cast votes. We find that aggregating these votes using our rules leads to a more equal utility distribution across demographics than making decisions using a single global preference model.